Regularized algorithms for applications in microwave thermometry - Alsaberi, Rani (My University, 2024)
This study explores the optimization of the regularization parameter for Tikhonov’s functional, which is derived from the vector wave equation, a partial differential equation (PDE), and transformed into a volume integral equation. Solving this equation using Tikhonov’s functionals provides three different approaches, each with varying numbers of regularization parameters. To identify the optimal regularization parameters, three methods were employed: the L-curve method, the fixed point algorithm, and Morozov’s discrepancy principle. The L-curve method and the fixed point algorithm both indicated that a regularization parameter of 1 is optimal, yielding acceptable results across various reconstruction scenarios. However, Morozov’s discrepancy principle consistently produced superior results, albeit with a significant dependency on the initial reconstruction matrix. Ultimately, while Morozov’s discrepancy principle shows the most promise for optimizing Tikhonov’s functional, it is not yet viable for practical use without further refinement. Moreover, compared to previous studies with a similar setup, this study employs the finite difference method, unlike past works where the finite element method was employed. The code can be found at the link given in [28].
Keywords: Tikhonov’s functional, regularization parameter, L-curve method, fixed point algorithm, Morozov’s discrepancy principle, hyperthermia, ill-posed problem.